(2x+7)(2x-1)=9

Solution for (2x+7)(2x-1)=9 equation:

(2x+7)(2x-1)=9

We move all terms to the left:

(2x+7)(2x-1)-(9)=0

We multiply parentheses ..

(+4x^2-2x+14x-7)-9=0

We get rid of parentheses

4x^2-2x+14x-7-9=0

We add all the numbers together, and all the variables

4x^2+12x-16=0

a = 4; b = 12; c = -16;
Δ = b2-4ac
Δ = 122-4·4·(-16)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*4}=\frac{8}{8}
=1
$